Video: Evaluating the Input of XOR Gates

The diagram shows an XOR gate. If input A is 1 and the output is 1, what must input B be?

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Video Transcript

The diagram shows an XOR gate. If input A is one and the output is one, what must input B be?

Okay, so in this diagram, we see that we’ve got an XOR gate, otherwise known as an exclusive-OR gate. We’ve been told that the value of input A is one. And the output is one as well. And based on this information, we need to work out what input B is. So to do this, we need to recall the truth table for an XOR gate. So here is the truth table for an XOR gate. We’ve got the two inputs, input A and input B. And we’ve got the output as well.

Now, there is an easy way to memorize the truth table for an XOR gate. and that is to remember that an XOR gate stands for an exclusive-OR gate. In other words, we only get an output of one if either input A or input B is one. But only one of the two inputs can be one because if both of the inputs are one, then the exclusive-OR gate returns an output of zero. And so exclusively, one of the inputs must be one, either input A or input B. And that’s why this gate is known as an exclusive-OR gate or an XOR gate.

But anyway, coming back to the question, we see that we’ve got one for input A and one for the output. So we’re looking at the third row of this truth table, one for input A and one for the output. Based on this row, we can see that the value of input B must be zero. And hence, we found the answer to our question. For an XOR gate, if input A is one and the output is one, then input B must be zero.

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